What is the time complexity of Find Nearest Point That Has the Same X or Y Coordinate?

The optimal solution has a time complexity of O(n).

What data structures are used to solve Find Nearest Point That Has the Same X or Y Coordinate?

This problem uses Array. Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Find Nearest Point That Has the Same X or Y Coordinate?

The problem requires iterating through the points list and checking the validity of each point based on shared x or y coordinates. Manhattan distance is used to determine proximity, which is simply the sum of absolute differences in x and y coordinates.

Which companies ask LeetCode 1779. Find Nearest Point That Has the Same X or Y Coordinate in interviews?

This problem is frequently asked at DoorDash.

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Find Nearest Point That Has the Same X or Y Coordinate - LeetCode 1779 Solution

Find Nearest Point That Has the Same X or Y Coordinate - Complete Solution Guide

Find Nearest Point That Has the Same X or Y Coordinate is LeetCode problem 1779, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

You are given two integers, x and y , which represent your current location on a Cartesian grid: (x, y) . You are also given an array points where each points[i] = [a i , b i ] represents that a point exists at (a i , b i ) . A point is valid if it shares the same x-coordinate or the same y-coordinate as your location. Return the index (0-indexed) of the valid point with the smallest Manhattan distance from your current location . If there are multiple, return the valid point with the smallest i

Detailed Explanation

The problem asks you to find the index of the nearest point in a given list that shares the same x or y coordinate as your current location (x, y). The "nearest" point is determined by the Manhattan distance (|x1 - x2| + |y1 - y2|). If multiple points have the same minimum Manhattan distance, return the point with the smallest index. If no valid point exists, return -1.

Solution Approach

The solution uses a single loop to iterate through all points. For each point, it checks if it's valid (shares the same x or y coordinate). If valid, it calculates the Manhattan distance. It maintains a minimum distance and corresponding index. The index of the point with the minimum distance is returned. If no valid points are found, -1 is returned.

Step-by-Step Algorithm

Initialize `min_dist` to infinity and `ans` to -1 (representing no valid point found).
Iterate through each point `(a, b)` in the `points` list using its index `i`.
Check if the point is valid: `a == x || b == y`.
If the point is valid, calculate the Manhattan distance: `dist = abs(x - a) + abs(y - b)`.
If `dist < min_dist`, update `min_dist` to `dist` and `ans` to `i`.
After iterating through all points, return `ans`.

Key Insights

The problem requires iterating through the points list and checking the validity of each point based on shared x or y coordinates.
Manhattan distance is used to determine proximity, which is simply the sum of absolute differences in x and y coordinates.
The algorithm needs to track both the minimum Manhattan distance and the index of the point achieving that minimum distance. The index is crucial because we need to return the index of the point, not the point itself.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(1)

Topics

This problem involves: Array.

Companies

Asked at: DoorDash.

Find Nearest Point That Has the Same X or Y Coordinate | LeetCode 1779

Easy

Array

Time: O(n)Space: O(1)

Solution Code

Available in:

class Solution {
    public int nearestValidPoint(int x, int y, int[][] points) {
        int minDistance = Integer.MAX_VALUE;
        int minIndex = -1;

        for (int i = 0; i < points.length; i++) {
            int a = points[i][0];
            int b = points[i][1];

            if (a == x || b == y) {
                int distance = Math.abs(x - a) + Math.abs(y - b);
                if (distance < minDistance) {
                    minDistance = distance;
                    minIndex = i;
                }
            }
        }

        return minIndex;
    }
}

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Problem Info

Description

Problem 1779: Find Nearest Point That Has the Same X or Y Coordinate - Detailed explanation and solution approaches.

Topics

Array

Companies

DoorDash

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:1779

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

6 steps

1
Initialize `min_dist` to infinity and `ans` to -1 (representing no valid point found).
2
Iterate through each point `(a, b)` in the `points` list using its index `i`.
3
Check if the point is valid: `a == x || b == y`.
4
If the point is valid, calculate the Manhattan distance: `dist = abs(x - a) + abs(y - b)`.
5
If `dist < min_dist`, update `min_dist` to `dist` and `ans` to `i`.
6
After iterating through all points, return `ans`.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(n)

👍 Linear - Good! Visits each element once.

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The dominant operation is the iteration through the `points` array. All other operations are constant time. Therefore, the time complexity is linear with respect to the number of points. The space used is independent of the input size, so space complexity is constant.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Using a Priority Queue

Calculate the Manhattan distance for all valid points and store them in a min-heap (priority queue). The point at the top of the heap would have the smallest distance.

Time: O(n log n), where n is the number of points. Log n factor comes from heap operations.Space: O(n) to store the priority queue.

Trade-offs: This approach is less efficient than the linear scan for this problem. It is beneficial only if you were doing further operations on nearest points, making the sorting worthwhile.

✨

Key Insights

1The problem requires iterating through the points list and checking the validity of each point based on shared x or y coordinates.
2Manhattan distance is used to determine proximity, which is simply the sum of absolute differences in x and y coordinates.
3The algorithm needs to track both the minimum Manhattan distance and the index of the point achieving that minimum distance. The index is crucial because we need to return the index of the point, not the point itself.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Edge Cases

Empty `points` list: The algorithm correctly returns -1 because no valid points exist.
All points are invalid: The algorithm correctly returns -1 because no valid points are found.
Multiple points with the same minimum distance: The algorithm correctly returns the index of the point with the smallest index among those with the minimum distance.

⚠️

Common Mistakes to Avoid

✗Forgetting to check for valid points before calculating Manhattan distance – this could lead to incorrect distance calculations.

✗Not handling the case where no valid points are found – forgetting to initialize `min_dist` to a sufficiently large value or failing to return -1.

✗Incorrectly handling multiple points with the same minimum distance – not selecting the point with the smallest index.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Finding the nearest facility (e.g., hospital, store) that is aligned with a specific street or avenue (same x or y coordinate).

🏦Locating the closest sensor in a grid-based sensor network that reports data on the same row or column as a reference sensor.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

Even for easy problems, discuss time and space complexity. Interviewers want to see you think analytically.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: November 7, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

In a real interview, always clarify constraints first. Ask about input size and value ranges.

@TechLeadJul 13

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jul 6

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJun 29

❓

Frequently Asked Questions

When should I use in-place modification vs creating a new array?

Use in-place modification when space complexity matters (O(1) space requirement) and the original array can be modified. Create a new array when you need to preserve the original data or when the problem involves significant restructuring that would complicate in-place logic.

What should I learn from easy problems?

Easy problems introduce core patterns that appear in harder problems. Master basic operations (iteration, conditionals, simple data structures), recognize common patterns (counting, searching, basic transformations), and practice explaining your thought process clearly.

What is the importance of time and space complexity analysis?

Complexity analysis is crucial because: 1) Interviewers always ask about it, 2) It helps you choose between approaches, 3) It demonstrates CS fundamentals. Always state both time and space complexity, and be prepared to explain how you derived them.

What is the optimal approach for "Find Nearest Point That Has the Same X or Y Coordinate"?

For this easy-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether standard techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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